Does one's ablution become nullified by passing wind after fully donning one's socks and completing the ablution, or by entering the restroom before prayer time, such that one must remove the socks and repeat the ablution, or is it permissible to wipe over the socks?

It is permissible to wipe over socks if they cover the obligatory area (for ablution) and are thick enough to allow for continuous walking. Some scholars do not require them to be very thick or robust. If they are worn after a complete ablution, and then a ritual impurity occurs, there is no need to remove them. Instead, one performs ablution and wipes over them, provided the legally prescribed period for wiping has not expired: one day and one night for a resident, and three days and nights for a traveler.